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     "source": [
      "FIR filter\n",
      "======================================================================\n",
      "\n",
      "\n",
      "This cookbook example shows how to design and use a low-pass FIR filter\n",
      "using functions from scipy.signal.\n",
      "\n",
      "The pylab module from matplotlib is used to create plots."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#!python\n",
      "\n",
      "from numpy import cos, sin, pi, absolute, arange\n",
      "from scipy.signal import kaiserord, lfilter, firwin, freqz\n",
      "from pylab import figure, clf, plot, xlabel, ylabel, xlim, ylim, title, grid, axes, show\n",
      "\n",
      "\n",
      "#------------------------------------------------\n",
      "# Create a signal for demonstration.\n",
      "#------------------------------------------------\n",
      "\n",
      "sample_rate = 100.0\n",
      "nsamples = 400\n",
      "t = arange(nsamples) / sample_rate\n",
      "x = cos(2*pi*0.5*t) + 0.2*sin(2*pi*2.5*t+0.1) + \\\n",
      "        0.2*sin(2*pi*15.3*t) + 0.1*sin(2*pi*16.7*t + 0.1) + \\\n",
      "            0.1*sin(2*pi*23.45*t+.8)\n",
      "\n",
      "\n",
      "#------------------------------------------------\n",
      "# Create a FIR filter and apply it to x.\n",
      "#------------------------------------------------\n",
      "\n",
      "# The Nyquist rate of the signal.\n",
      "nyq_rate = sample_rate / 2.0\n",
      "\n",
      "# The desired width of the transition from pass to stop,\n",
      "# relative to the Nyquist rate.  We'll design the filter\n",
      "# with a 5 Hz transition width.\n",
      "width = 5.0/nyq_rate\n",
      "\n",
      "# The desired attenuation in the stop band, in dB.\n",
      "ripple_db = 60.0\n",
      "\n",
      "# Compute the order and Kaiser parameter for the FIR filter.\n",
      "N, beta = kaiserord(ripple_db, width)\n",
      "\n",
      "# The cutoff frequency of the filter.\n",
      "cutoff_hz = 10.0\n",
      "\n",
      "# Use firwin with a Kaiser window to create a lowpass FIR filter.\n",
      "taps = firwin(N, cutoff_hz/nyq_rate, window=('kaiser', beta))\n",
      "\n",
      "# Use lfilter to filter x with the FIR filter.\n",
      "filtered_x = lfilter(taps, 1.0, x)\n",
      "\n",
      "#------------------------------------------------\n",
      "# Plot the FIR filter coefficients.\n",
      "#------------------------------------------------\n",
      "\n",
      "figure(1)\n",
      "plot(taps, 'bo-', linewidth=2)\n",
      "title('Filter Coefficients (%d taps)' % N)\n",
      "grid(True)\n",
      "\n",
      "#------------------------------------------------\n",
      "# Plot the magnitude response of the filter.\n",
      "#------------------------------------------------\n",
      "\n",
      "figure(2)\n",
      "clf()\n",
      "w, h = freqz(taps, worN=8000)\n",
      "plot((w/pi)*nyq_rate, absolute(h), linewidth=2)\n",
      "xlabel('Frequency (Hz)')\n",
      "ylabel('Gain')\n",
      "title('Frequency Response')\n",
      "ylim(-0.05, 1.05)\n",
      "grid(True)\n",
      "\n",
      "# Upper inset plot.\n",
      "ax1 = axes([0.42, 0.6, .45, .25])\n",
      "plot((w/pi)*nyq_rate, absolute(h), linewidth=2)\n",
      "xlim(0,8.0)\n",
      "ylim(0.9985, 1.001)\n",
      "grid(True)\n",
      "\n",
      "# Lower inset plot\n",
      "ax2 = axes([0.42, 0.25, .45, .25])\n",
      "plot((w/pi)*nyq_rate, absolute(h), linewidth=2)\n",
      "xlim(12.0, 20.0)\n",
      "ylim(0.0, 0.0025)\n",
      "grid(True)\n",
      "\n",
      "#------------------------------------------------\n",
      "# Plot the original and filtered signals.\n",
      "#------------------------------------------------\n",
      "\n",
      "# The phase delay of the filtered signal.\n",
      "delay = 0.5 * (N-1) / sample_rate\n",
      "\n",
      "figure(3)\n",
      "# Plot the original signal.\n",
      "plot(t, x)\n",
      "# Plot the filtered signal, shifted to compensate for the phase delay.\n",
      "plot(t-delay, filtered_x, 'r-')\n",
      "# Plot just the \"good\" part of the filtered signal.  The first N-1\n",
      "# samples are \"corrupted\" by the initial conditions.\n",
      "plot(t[N-1:]-delay, filtered_x[N-1:], 'g', linewidth=4)\n",
      "\n",
      "xlabel('t')\n",
      "grid(True)\n",
      "\n",
      "show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
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IbiEeuZC0uNkiF49cSCYkkDtAd19Nd32gj0feUvphsh/DeKC7PvCHRifEMkKQIMSNQCDI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\nIAiCIAiCIAiCIAiCIGjC/wGAP51xv78zTAAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f79b3c3abd0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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NZZwHjLGsRBquuAKCg5PJzEwgPT3veqHO64iqvFdw4sSJAmmnTp3K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\nIiIiIiIiIiIiIiIiIuaX/wETgTbYMHZM+AAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f79a8853610>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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uk0cnpsKe0ZCTIyJqhz2Li6dcLG2rt60fINwXXTSwG+KVV2o9IMZrTzLJFHui\nhVtNlUQL90SIuMvRctc+oCxq278BcxHC/sA4viP5JCDH7XaLvtunTNMI5dhYaj80QLh37BBTHA3H\nd74jBnsYxI8q3EeP97K/eb+0bVHpokE+kX5UQbDZ4Irpcstpa956KVXS0gJvvSVGU0azfj088UQK\njD1HqG8KsHnBct6Z+kn+XPc9jlmej1ynGTNGTqOlivE0TrYiGh4BXEBLzPYQIgf+5FAHuP3225kW\nLlybn5/P0qVLI7+Eag4q6cs+H5SX8/DDD4/5+91uaGmp4eRJaF9czaVHX6em5iwNDWL7G2/ApZfW\n8OUvwy9/OfTxxCqxPB57krGsd3tef11sf/tICT39PRBuPKxYVEGJs0SX50f0Ba/GZoO8hjxh83Rh\nt6/7n7S0rScYFIL+m9+Iz3d2yseDarZuzbzrpVd7DjQV0pKzk5YTOzlUD45JU8nJuYmamhpKS+EH\nP0jc9+/atSuif6nkU4g8N8Dnw8sl4WW1F+M84N4hPq/ogi98QVH+3/9TNm7cOOZDdHYqisulKGvW\nKMr+//u4sr70VmX9em37448rCijKj340/HFAUUwm8X489iQDvduze7c4fx994CmF+4n8XfPHa9Ji\nz2i4915h88svK0p/qF+x3Vsk2f6jP25VrrxS7Pvtb4t9X3hB+3woJNZVVSXGnmSSKfZcfeefpWtQ\n8vVrlb//Pfn2AHF1ZxhPquSPwBREo2QVsA/4JTAN2AF8FVgD/HAc35F8EpDjdrlEY6THAz0XVbO0\nswZPp3Yd1LSJzzf0MdReKOqIq/HYkwz0bo+aUjjSIadJFpbI04Olyp7RoD6CL1wIZpOZWVmXSdsP\n9b8a+b/q6sRrdI5b7UWjponGa08yyRR7zvbJM2HZfQsGDKbRA+NJlSjAPeH3z4RfPxZ+1WdScTAS\n0KvEbNbKOboXTaMnx41p9y64SYyI83jE9uGEu6dHvBq9CMaGKl5nQ7JwLyhZkAZrRocqvFOmiNcl\nrmvY59VKS25qeYbCoHhg9fvFwJ9o4fZ4RC8HY3b4xNFqlv0nx6NP4TZGToYbJ4fq1zla3G7Rfaio\nCI4uuJ781/8W2eb1QmXlQOFWFFEBDrRZw7u7xfrx2pNo9G6PGpl6cuSIaX7J/LTYMxqOHBGvpvAI\niMsqbsCkaOWFj/n20ZkjhMTvh0mTxCQOKuroymBwYPlXvV+vdDOUPZ0x/mPpmG8Ity5J0ERwbreo\n/pWbC635yYWtAAAgAElEQVSX3sisXc9G8h8ez+DCfffdokfBqVPixnS7RfSuirnB6AkEIK+gj277\nYWn9/OLUCPdYWLpUTI+mMq20hPz2y6V9WsvEw6zfL3xosIhb/cE3GB99oT66bLL/mNsM4dYn4ZGT\n483Bud0i2jaZwHbZRZgDXZGpcFThjq1hsmePiJQaG7WIW+0Tnik5wXQRa4/fD+6px1DM2q9euauc\nAntBWuwZDXffLc+WVFgIzpMfk/bpnPokISU0aMTt9YpAwekcKNx6v17pZjB7jrXJ/pPtL6ffV2AI\nty5JUMTtcmk1eKdMM/OM43aUX/0aEMI9adLAiPvYMSgrEzegKtwOhxE9jYVAAHImZU5+ezAKC6H/\nvRvJMmlNT315h1l3bF1EuGMj7txcbVotg/ER2/8/q32BNABHTxjCncAct9ojZMoU+H7bv9Dxm79A\nUxMej2hYihbu/n6RIlm8eHDhzpScYLqItcfvB1NJTH47hWmSRJyf0lJoO1PEKtdHpPUPvv4g3X5l\nSOEeLOLW+/VKN6o9Bw/CtdeKdQdaZP+heb4h3LolgTluNeJ2OqGJMv7I/yL0wIMDctxf+YrYt7dX\n3KyqcDscWqrEID4CAejNz+yI224XOeuF3n+V1r915i1aqh5nyhQxJFslOuI2ntLGxl//CmvXivex\nEXdvg34j7lSUddUv/f2iSd5uT0iOOxpFgfMn38uXnlnE3OybsRcvpD2ngVeO1PNSw2lCVx2i39/F\nkbJpzGy/mbKyOdjtkUnnMyInmE4Gy3F3O9IXcSfq/EydCu17VzFj3oc4btEKO7de+EXe7A1Q55jO\nf289xdH2Q2xu78aZPw1T8c10dcm1aPV+vdKNak/0D2FsxG1qmY/Xawi3/ujqEuGKyTTyviPgdg+8\nwOXnFbPjwj/w1V9+hIvfaoOb4QNPAlE1j7YB29u/w4eO/itW+49RlGwjehoD/kCIDot842VaxA1C\nuPfsgesWPcSj2a/h7wt3UM/q4Z63vwy3wldejfpANrD6O/z84J1cfOmPyDaf27d0vKjCHVJCHGiW\n/cftX0BHjygGpjfO7VRJVIGp8ebgPvlJuPVWed38+bDJdjUP+n877GcVFP7e/FPem/k5HE6Fri79\n5gT1Qqw9jYHT9Jm0IYTZvYWUOkvTZs9YmToVDh+G6bmzeeS6R0b3IZPC840P8eHHP8c11yoJtSdR\n6NWexvBESac7T2s/kkCBrYCcPuE/hnDrjQTltwGWLRMNjdHMmAGHDsH6wE3Ys+0jHuNk/u9prPiD\nEXGPgYY+OT/pDszHlIAnqVSj1hzKzYVPL/00ztcexZY1ulkgXjzze2ra/zBgMI7B0KgRd2x+e0HJ\nApoaTVitYmyF3tChSSkkSriTkYObPBm2boVJlSbmFc8jq20+q4ovx3b4Nh6sfpCfXfMzCrKqpM/s\nLr2LVp9HtzlBvRBrT5MiP+YW9KU2TZKo83PTTfC978HVV4vlvON38OK1+7G8/W2unHElU/ovZ27g\nNu679EFmHvkZJVbZf3qq72L3IcN/RkK1Ry21vL958DTb+fI8zrrh3E6IJTDiHoyqKnjvPVizBmq+\nsJPp0+Hffgr37oF71oh9Qoev5ZvHzidkFmO2g1mtrG37b77Ct5Nm10Sk1SRHTMWKfkdMDsekSaIu\nu4rVCq6+6eS/8wP++YroAfGpT8HCZWDbBT/90rXcvO58+kzhMf+OVv7z9f/mT/MN/xkNaqmE9xpl\n/1Ebtj/5yVRbNDrO7Yi7q0v0vyM5ObiqcDA0PVxjubBQzFai9vcGmFc8j+n135I+93rg57y2/rWE\n2zMe9JqjVGnPliOmUnNqhTtZ58dqFaMl7eFM2zXXwNe+Btu2ickVVk6fx0WK7D9/bzT8ZyRUe3p6\nRCokNuKeXzKf/n7RdVePnNvCneSIu6QELBZZuA8d0vp7Q7j/95Gvk6Nodng5y9t1byfNromGoih4\nrPKNV5mTmRF3LDYbdHRowg2wcqVIwalFzS6zfx1LlP/4DP8ZNb29kJuncKh1YFdSPea2VXRsWgpI\nco7bbBaPvqpwFxWJHgPREbfbDf72fOb0fEL67G67PG9iutFrjhLgrO8sfdkdkeWsfgfl9slpsyeR\nWK0DhXvFCnjjDREU5ORAkTOfOQHDf+KhurqaUAj6+sBefJbOHs1/HBYHk/NS6z/xYgh3EiNuEBO8\nqhXgCgtFzruiQtvudosRcLO8n5E+948j/6C71+heMhpiB05YffNxOiaGa9vtIrKOFu7CQjH8QK1B\nnpsLk1tl/3nxgOE/I9HbK374zGWDRNsmffuPvq1LNlHCnawc3J/+pHUTLCwUtSYmR/2Y5+YK4XZ7\nVlOYpW3oPtzNa8f1k6fUa44SGDBwwtw6H4cjffYkEpdL9Hywx/QmXbZMe19UBNStxuTR/Cd4vJv/\netHwn6GoqamJCLdSnJ4a7uPh3BbuqMbJVFBYKF6ronpw5eUJ4Q74TazKvVHaX0/CrWdiI+6+htQL\nd7JwuURf41jh/sY3xNMcCOE+fcpE1hHZf57YbPjPcPT0iHRTX376SiWMlXNbuJOc445FzW1HR9w5\nOcJ5zp6FlUVXahumw/oT61EUuSJcutBjjlIldvBEoDb1wp2s8+N2C9+IjS9uvBG2bBHvi4vFbDqF\nnbL/nMlZnxSbxoIe/acnPJw9mDd4V0A9c24Lt9eb9Bx3NINF3AD5+aI295qpazBHXZL9zft5+HcN\nUmOmwUAGlONsmVgRd12d8JGhKCoS+dopoTVSbtZn30+DtyEFVmYmqnD7nUaqJLPo7IzcEanIwRUW\nipx2bq68Pi8P6uthanke8/NWipUnxMv/bNmQdLtGgx5zlAAdgQ7O+s5G1psVC7TNnFA57ro64SND\nkZ8f7sFUlMfKStl/Npww/Gcw1By32dFBT47mP1lYmFkwM42WjY5zW7jb24cPZRLMjBla0fZo1Juy\nqAguqrhC2rbfr5/HXT0S2zBZYZ0NIcuEiri7u4cXbrMZCgpEbfcrpsv+s/6E4T9D0dMDxDRMFptn\nY8mypMegODi3hbujIyLcqcjBVVTAX/4ycL0aMeXlwZrJ4Rsv3Pc7ULIlEVVnx40ec5QwME2i5icn\nUo4bhhduED/6ZWVwxQzZf7bUbkmKXfGiR//p6YH+wpiBWxb9p0nAEG4RqqSZvDyRRjGb4cIpqyEU\ndVmKD5PlaicYTJ99eia2YXLFVHHjZU+QKjxqE8xIwl1cLIR79aTVUp77cOth2v3tw3zy3KW3d+Cs\nSVU2Q7j1T1TEnc4cXF6e1uOkNN+JqXVhJEcJYJ+5A48nPbap6DFHCQMj7sUVC1izRoxYTYc9iWa0\nwj1pkpjr1JnjZGGJ7D876nckxbZ40KP/9PRAMFf2n+nOzJh849wVbkURjZMj3REpID9fE267HZTa\nVdL27Cnb8HrTYFgGEJvjnl8yn5oaXTxIJQRVuEdqivnDH+CDHxTvV02S/Wd7/fYkWJb59PRAwBUj\n3G4j4tY3Pp8oBGERDRHpzMFFR9xZWZDduCqSowToL9+e9ohbjznK7t5uTnacjKwzYWJu0dy02ZMM\nRhtx2+1awf9Vk2T/2Va3LSm2xYMe/ccb6CZgO6mtVEzMyk+P/8TLuSvcUWmSdFNUJHoEqDja5YjJ\nX7SVzk4lxVbpn0Mth1DQzsu0/GnYLSPPNJRJjLZxMprYiHvDoa1c+37Df2I54T0EJu28WP3TyHNm\nhv+cG8Ld369VTFeJEe505uD+1/+CH/xAW3b7F2I+oXVJ6rWe5URrXRos09BjjjK2YTKdAyfSneOO\nZmHJQiynNf/xcpa1b9Zx8GCCjYsDPfrPca/sP1bv/AGlBfTKeIQ7G3gQuBH4NhDdae1y4KvA14BV\nAz+aQpqbxay9a9YIAVfRUcTtdMoRt9Nuwe6fLe2zr+XdFFulHx5/HG6+WV63cye8/M4ead2i0kUp\ntCo1qMIdO2hrOCxZFmYXyv5D+bvU1ibOronAiW7Zfyxti7CNbnrPtDMe4f4ccAZ4AWgDbgmvzwJ+\nDPwC+Dnwg0E/nSp++EO44gqRPH72WW19e7sUxugpB5efD729a6R1Rzx7htg7NaTz/LzxBvz1r9py\nSwt84xvVvLJTPieLy2Jma04hyTo/+fnw1a8K942HNdWy/1C2J62TUOvp/gJhz8kY4TY3Lz4nIu7V\nwK7w+93AdeH3U4CWqP36kJpKksD+/XD//fDkk0hTXHd0iHDtnntEPuLll7VtTU2i46sOef/7oadW\nFqGTgfQKd7JQFHjuueH3mRtuLzpzRry2tIjBTJ1W/Qh3ssjOhp//PP7PxZ4Lc+UeuroSZFSGUFcn\napkPxeke2X+Us4vPiYi7HFA7qfmAskHWE34fv0J6vSLU+Jd/gf/9v8X012vWwIc/DPfeCxs2wPbt\ncMcdUF0txgU/9BB84QtCDQB+9zsxxryyUkyb/dpr2rb6erE+jJ5ycJ/8JOS290nr6vrSK9zJOj+n\nTsFHPjL8Pj094nVHuDtyZyc4Cv+G4q6P7GMKWdLWowT05T8Afcdl/zFXpDfiTsf5+cEP4Pe/H3zb\n3179Gx39sv/0np2bMRH3eMaXtQLhNm9caFF2a3iZqG3Ngx3g9ttvZ9q0aQDk5+ezdOnSyCNVzZtv\nAlC9ZAlYLNTU14PbTXVVFezcSc3XvgaBANUf/SgcPkzNrl1w2WVUP/AAfPe71Fx4IXz/+1Rv3CiO\nV1sLoRDVhw7BvHnUbN8OM2dSHbZl1y7x8BD5/rCjpWN59mz45me93HOQyLNK68lDrH1tLddceU1a\n7EvW+XE4xPKGDTWYzYPvL0aN1vDOO3DjjdV0dkIga50YZBI+P9aDU9jyxpa0XT89+Q+A95RXOj99\n7Yd4Z9daPsvE8p/hlt97D8rKBt++bss6qCVyfiz7p9Dt3YLNlhr7Hn74YXbt2hXRv3gZTxWMTwFW\n4LfA54EA8ApCpN8ALgkff1P4fSyKoiShi1JzM1x8sUiT3HabiMJVPvEJuOoq+Mxn4EMfgs9+Fm64\nIfE2JIgZ/zWDEx3aELjtn9vO5KwVuFwpnf8hqbzwgniY6u4eOFmAyl13icv4+ONw++3w9NPwgw3/\nxe6Kr0f2qWz+FHW//ENqjM4QCu6fQYdJ858vW7bzy7tXpNGi1HLFFWJi5R/9aOC2/3r7v/j6Ws1/\nco9/Cs8Tf6C/n7RMEmwSBYlGrcfjMfGPiHz2LUAVsA/4ZXjbt4FvAHcC/zaO74ifkhJ4911Ytw7+\n8z/lbRdeCG+9Jd7HpEr0yJLyJdLynsY9TJ0qfnMmCnXhXo6xvTWjUeu0qK+dneB3y6mjgp6Jl98e\nL5VZsv+cmqDtJEPR2qrNy6ny0EPw6KPiXoqmr36xmH8yQzpIj8dMBbgHeAa4F9gJfCy8bTPwUPgv\n9eXJHA4xQ29sWb0LL4RwCkbPOW4Q9iwulcVo99ndBIMQzv6k3J5koAr3cEW0AgFR8F7NdXd0QFPj\nJmmfor70dgXUo/9Mtcn+U9eXvpnf03F+2toYkNdftw727oVNr8v+031iUWSik0wgQ35fEsSSJXDy\npOiW0NKi214lKovKZDHa37KfBZlRA2fUqD1Fhou4AwHRj1kV95ZOP53m49I+ZaFlg3zy3GamS/af\nJvYPsefEpLVVFm5FgXfegbomP8c7ZP+hYZk0lkLvnFvCbbHA8uXwy1+KQTlRtT/VRgO9UF1dzYIS\nWaX3N++PzFeZ6nkok3V+6sMN+yOlSnJztYj7mG8XynSt22dx1gzyLMVJsW+06NF/ZufL/tOWlT7h\nTvX5CQSEaEcL9+nTQsxP+HcRmqr5z4yCGZj8xYZw65qLL4aHH4Zrrkm3JSMyq3AWWSZt5EW9t57u\n/k5AHxMIJwKfT7zGE3Gf6pOLJk0xr8JqTZKBGczsolkQ0vzHn11PZ6AzjRalDrX/drRwHzoE5eVQ\nh+w/qyatwuHQ/QO4xLkn3HfeKa7e9ddLq/WYo8zJymFW4SxpfXu2KDiR6okVknV+enrEg89w/48a\ncav71Ju3SfWmCwMr0y7cevSfwrwczB2y/xxsSU/BklSfn8GEu7ERFi+GdofsPysrVw4oO6F3zj3h\nLiqCAwfgksF6KOqP2HRJZ46oH6ymDTKdYFBUHoiOuKNLyoDYlpen/c9tdjliMtWvypgRb6nE5YJQ\no+w/sRNPTFRaW0UfheheJU1NIkPaUzJ4xG0It94ZZBJHPeYoQZtDUaXLfgC3O/URd7LOT0+PiKZV\n4VYUEYE//7y2T3SqpM3fRsBxVCuiEMqidtv5lJcnxbxRo0f/cbuBZtl/YieeSKU9qcTnE6mP2Ig7\nr7wNCjX/MZPF+eXn43QaqRKDBBJbqtTv2k9eXuqFO1moaRBVuNUn6tOnB+7T0wNbTsu9S/OCCzn8\nnjPlU5VlAm430CL7z/6Wc6NnSTAoZkGKFe4Ot+w/VTkLceY4jVRJpqLHHCUMjLh7cg9I+d5U25No\n1Ihb/X+2bhUR9/Go3lpqqiQYhPUn1ouV4RzlVC4lFEr9HJOx6NF/XC50E3Gn+vwMJtxNTXAqS/af\nhe5LAVEWaVV6C1DHhSHcOmde8Txpud99AndBYMLmuL1eWLYMjh2T91HFPSLcYRa5rgDSL9x6xGIB\nWmT/OdFxgkDfMF14MoSLLmLY6fyCQVESNzbi3tct+8+yfOE/t90mBl1nCoZwh9FjjhLErN1Vrqna\nBnOI7LLDEzbH7fHA+efLwq3muD2hRvY17RMrp4PZZOaC8mrMZowcdwwRe3qdTHZr/hNSQhxuPZw+\nexKAoojCoI2N8vojR7Tin9HCra5r8DZyzKv5D4qZlSWJsyuVGMKdAcwpkB93Q4UHJlyOW/1/vF7R\nZevECe2GU4W7wbZB+uzyiuXMqMynvFwaS2UQhaLAwjJ9pEsSRXc39PXJYxkURaQ6Nm8Wy8Gg6FVi\nsWi9kVrcsv+4PMspduljFqx4MYQ7jB5zlCrzYnuWOPdPiBx3f7+Y98LplFMlZWVCiNXC/6q4N7nW\naR8+AVdMv4L58/UxlkrP/hPbThI7V2cqSOT56egQr+3t2roTJ8T6p58Wy8EgWK1CvLu7xXL/NNl/\nnE1XpL3//1gxhDsDWFgq98X1Wg9MiBx3T4+4uWw2OVXidou8d2eniKQCAXC4emku/Lv0+atmXsX0\n6fDYY2kwPoOIHQuQ6X25O8ODP6OFe9cumDoV1odT2LHC3dbRC3Nk/7HVXZWx/f8N4Q6j2xwlsKhC\njpg6c1KfKknG+QkGRdW/aOH2emXh7usT8y3u92+gL0d7Ni5cUMglU/QziErP/hMbcadDuBN5ftSI\nOzpVsmsXXH65JupqUGC3iye3dUc2oNi1D9inF5J15hJDuA2Sx8LSGOHOOkx3oG+IvTOH6Ihb/SHy\neERaJDdX3ISBgNjn5QY5rL5h7g1YsixpsDrziB0LcLj1MH2hzPWfwSLuTZvEHCne8KSJasRttwsf\nevKg7D9zQjcQ9FuMVEmmo+ccZaG9ELq00QH9ph7OBo8P8qnU2JMoRhNxB4NgKTrDxobnpc8u8S8Z\n5IjpQ+/+U+rU/Kenv4fj7ZnrP7E5bq9XlGu97joRXSuKJtw2G5xqr2VDvew/+YcWEwhgRNwGySW7\nXc5TNvRmdp4StIjbah1auAMB6Fn9A/qU3sjnLJ45E3JG92QyIM+dwT1LOjrED76aKtm8WUxRlpsr\nfEltjFQj7kcPy/5TmjWb3O4lBIOGcGc8es5RAlg65cfds/2pvfFSkeNWlIHC/fqpGroX/Er6XMmR\nu7jssssSbs940Lv/pDvPncjz09kpGiLViPvkSZg9W7x3uUSdElW4u0treLH+19LnP5D/TQoKLsvo\niNvo/Zoh2LzziZ4+r1nJ3IhJRY24j/ZvYGPZL5j0022E7gyx+rFKuspms6cpl71NfwKTNqn0JPsM\nys5+Oo1WZybpFu5E0tEB06drwv1Ww0a2V/ycqp9up+0z/Vz+lwp8RXOo7chj14L/QUHznxkFM7i6\n9NM84xXdUTO1/78RcYfRc44SwNklP+q2mFPbFzcZ5ycQUDi75C4ePHUF9bkv0OCrB9dZdjbs5JDl\nL2zr/y3+fnnSwH+d8wgOa47ur1e6ibVnsNmUUkmic9xTp0J7h8Jd6+7ij1mXc9D0AnXeOvodZ9nf\n/i6nc//CBs9v6M+S/edX1/2KXGcOx4/XYLMNWig0IzCEO0NwBeSIqT3rAIqiDLF3ZvDrQw/QOOOh\nUe+fVfN9FjuvztjH23QS27PkQHPm+o/HAxUVcGbm/Tz01uj957LQ97lq5lU4HCIll8l+ZAh3GL3n\nKJ1KBTmhvMhyn7mLWk9t2uwZKxs3wi9+AW/VvsUTJ/99VJ/J7s3nN9c9Sn/N3fj94obT+/VKN7H2\nVLgqsKH5T1dvF3/+R23KpsBL5Pnx+8FX8Bbti0fnPw5TPlf5H+W63LvFsgN6eqoztisgGMKdMdis\nJtzBzK858d3vwhN/VPj62q8TQpuwNTtYzC+Wb+T8mlNsun0TX6r6LefVPsw9s/5G9bu1fG7FHWRl\niYanTI6U0oXJZKI8S06XPPjIAXSW4RkVXd0Kfwt+XWr7KLQVs/HTG/nAoVPcP3UTs/b/hq/M+hnX\neV/gXnctU1vvEPXJEcLd1pbZfmQIdxi95yhdLsjpTF+eMhHn58wZeO892Ot/lW118vRRVdv+xHx7\nNfmmKVwy9RI+PO2zlBz/P5zvuB5XjgsQN1pHh2jQ1Pv1SjeD2VNli+mZ1Lefpqb02TNW6h2vciwg\n+8//3PQk1dOqKbVOYXLoEgpOfI7bZn2dhVk3oARdeL2iuyCI2jjd3TWGcBskH7cb+s9mds2JI0dE\n5T/TBQ9L66+YdAOW01fT3S2iIRA3l8+njZxU12V6pJROprsGzl/a3JwmY8ZBbaXsP5ZjN/D+OVcB\n4j7xerWupurISbUGDmg+ZqRKJgB6z1Hm5oLvRGKrvN1yC6POcSbi/Bw9CuVzawlUrZPWf+387xAM\nityl3S7WuVxiFFz0IAmHQ0wCa+S4R2Ywey6aI/sPJamLuBN1fmo7a/GUyv5TcvA7kfex/bjVMQLR\nEXdREYCo456pZLDp5xZuN3SfGpgqGU/PgA0boKFhvJaNnqNHoWvKs9K64uBKVletJBAQI95U4XY6\nhXAbEXfiuOZ82X8o2U9Tc2b1LHl2v+w/M20rKO9fGVmOjrhV4fb75YjbEi5xEzsRQyZhCHcYveco\nc3OBzinkmByRde2Bdpq6xh4yeb1aUZ547RkLR4/CEevT0ro5PR+PDHn3+7XHWDVyih7dFt2opPfr\nlW4Gs2dq/hSy+jX/wd5OXXtqQu5EnZ+n98v+cx4fJz9qLoTRRNxhi6ivT4hJacEQ7gzB7QYUM1U2\neQ7Bsea5g0Ho7RVOnioONZ7iiP9tad380EciN1d0qkSNuKNTJU6nSJVkcm4ynZhNZqbnyv5TF2fN\nm29/W0zonA5OdZzi7TOy/5S13iIJd2zEPViOG8REwplMqoTbPfIu6UXvOUo1WpjmHDnP7fOJ/tLD\noQr2aCPuRJyfxgK5QttU00UUWSZjtYofka4uTbjtdjEkvqtLTpU0NIhzoffrlW6Gsmf1DNl/Woiv\nneRHP4I1axJnTzw8f1D2n9zOi/CemTxoxB07SUdsxD19+vjtSSfjEe5c4HvAjcC/DrJ9AXAMOAJ8\nfBzfY4AWLczKH7nK26OPiqLyw6EK9miFOxF4Sv4pLc8NR9smk+gB0NGhpUpMpoH9bR0OIdz5mTlN\noC6IHfreZT9APM0k8+aRtvlO/3lc9p8qz0c4c4ZhI26bTZtJKfpJ7Wc/g4dGP+hSd4xHuL8DbAJe\nAEqBVTHbPwa8D5gN/GYc35MS9J6jVKOF+UXyjbe3aS9bt8K+fdo6NWodjngj7vGen57+HnoqXpfW\nVXRfjdMp3lutomhQtO2xqRGnU9yQeXn6v17pZih7YoVbKds7pmnw+vsTY89o6env4fWTsv9M7b16\ngHC7XNrMSWrlyaam2Pw2hEI13HnnuExKK+MR7tXArvD73cB1MdsnA9uBZwEjKzlO1Ih7ScUiaf3e\npr3c+nGFRYu0m0l10uEiqVRE3B4PkQagt05vg5yuyLacnnJs3gW4xNgabLaBwu1yad3/QIvGjYh7\n7Cwqlf2H0r0EAsJR+vtFymo41GhbrZ8OIi3x4osJNHIQttVto6tX859yVzkVlgWcOSPnq91uqK0V\nPmIyCX9qbpbz2xOB8Qh3OaDe9l6gLGb7/0ZE2yHgK4Md4Pbbb+f+++/n/vvv5+GHH5Z+lWtqalK6\nrK5L1/ePZM/hwzVADfPKpuO0OOEEcALa/G1MXlAP1PDEE2J/UfGshpdfHvr4mzeL46mRdzLOz333\n1XDvvWL5N888KmwOY9tzHsePvR6JuKGGEydqIuJcU1ODotREIu6amhpaW8Xx8/LGZs+57D/q9ukF\nsv9gb+NUWz01NTVcdVUN558//PFV4X7tNW37l74E119fw/r1yTs/j/5V9p/zus6js+N1enuFSKv7\nu1xw9izY7WJZjbjNZn1dr4cffljSv2RwDbBxkL86oCS8z62IfPdgnA88Msh6xWD0HDmiKKAoPp+i\nXPDoBQr3E/mbeuXLSna2omzbJvb9/e/FvocODX28554T+3zta8mz+Yc/VJSbbhLvV//qEsnmyg88\npnz4w4ryzDNi++zZirJokaI89ZT2+YsuUpSpUxXlj38Uy/ffL2w+fjx5Np8LxPrPH958WVEUcW4L\nCob/bFGRouTkKEptbdTxLhCf9XrF8nPPKcq99ybW5ksek/3nsZ2PKXffLb73xRe1/ZqaxLqVK8Xy\n7t1i+X3vS6w9iQaIq0P9aCLutcBlg/z9Glga3mdReD8LoD645IRfy4C34jEqHcT+GqebWHtyc7VH\nv8Wl8rRdTaY9zJolBrCA9jg73Ki4eFMlYzk/Ho/IN/b097CzSe5DFjp2BT4fkYhbrUPiiOpmrOa4\nY3c2nTMAAB/5SURBVFMlRo57ZIazJ9Z/9jbticzjuCqmperYMXj1VW05GBQRrj9qVg918l513cmT\ncPjw6O0ZiZ7+HrbWyf5zxYwrWLNG5LGnTdPWq6k3NX2i+k5sjltv1ytexjP/w0+A+xBC7QHeAD4I\nVAPPAf8P+CXil+SxwQ9hMFoKCuATnwCzmQHzLQby9jAZ7cZR84/DCbfPJ4b+JjPH7fUKMd7XtI/e\nkNYCNslVhbdhCl3FDJvjVuuVRDdOwsCb0CA+Yv1nf+ueSM2SUEjed+1aMcL22mvFcjAoamEPJ9xd\nXdq6RLCvaR89/Zr/5PirmJI3hSlXD+zhYrNBVhYUForl8nLZxonCeITbD/xbzLqXwn8gUiQZg977\n4Vos8D//I94vKZdnOM+atAdnX/wRd2Vlcvtxq8K9o36HtH7FpBW86GNAxO3zDWycVLeBiLhdLjHd\nlN6vV7oZzp5Y4T7UsSfyY9/VJe/b1KT5SCgkGi9zc+XGyY4OIZDRx4gVyvGcn1j/yfWtHGJP8VTq\ncmnCnZsL73vfwP9Lb9crXjJ0xrVzm9ieAX15B8lxBPD7hcKpN1BLi/y56JGJXq+InFIRcW+v2y6t\nXzVpJesdohEpujsgDEyVRG9zOrWGSYOxEyvcJ30H6fAFyMqyDSvcPT0iNeFwaNF1b68IFIqLtXXd\n3SJNlihi/afAv2LY/d1uTbhBDEZLV9/zZGEMeQ+jt5zXcPbk2fKwdE3VVpj78efujdw4waCI0KOd\n9c03xQ2nPgr7fPFF3GM5P5GIuyEm4q5cQWGhEIXoiBvkiFvNXUYPeVe7AmbS9UoHI/nP1DzNf/qV\nfva37qWoSHtqU4kW7tj6HyAi67w84VvDRdzjOT+x/lPSO7xwu1xyF0GLRXt6S4Q9esAQ7gzF5ZGd\nt9O1TUqV5ObKwq1WQlu/Xrx2dUFJycAbNZF4PBAy+9nXtE9av7xiORUVop+5KtzqbNvRfbQ/+lHx\nmpUlXgsKoLQ0efaeS6yolP1nb9s2CguHT5VE17hWgwRVuNUqfCCOkaiI29870H8mmZYP+5nYiHsi\nYgh3GL3lvEayJ79Lbv5vtW6TGifz8mThVsu3btggXtXeAdG5yvHYMxheL1C+m75QX2TdjIIZFDmK\nIo1GqnBvC09ooq4HmDEDbr5ZzOgNcMEF8PzzY7cnmWSaPasmyf6zv3PbkBG32td/sIi7o0P4UbSY\nq8Id3dA51vPz3BbZf2ifwZzJRcN+ZjTCrbfrFS+GcGcoRYHV0vLZ7K3DRtwNDaIXSfRNmJc3euEe\nC14v5EwbmCYBkV+3WEQEB+Lmv+mmgcd49lmRPwXR8GTkuBPD6kmy/xzybaWoaPiIWy3cNFTEHZ0q\nUZTEVJ78/uOy/1C3glmzhv/MT38KV1wx/u/WM4Zwh9Fbzmske8r6l2OOunytpkO0+0Vn3EBgcOGe\nOVO7MVXhju7WNR57BsPrBdvMGOGuEMJdXk7UqEnYuROeeWb0x86065VqRrJneeVyzCbNf+p7DmHN\n64j0HAEh1F6viJx7eoaOuPPyBkbcIKdLxnp+GrNihLt+ZOFeskT2rcHQ2/WKF0O4MxRXjotJOQul\ndad6hZOrohwr3LNmaTdVT4/WrWsck+gMiaKIm76/TO4RsHKS6MpVUSHfXFarlss2SD6uHBcLS2T/\n8eXuCE+kK5bb2kS7wmA1rqMjbjVVEtulMBF9pz1u2X+oXzmicJ8LGMIdRm85r5HssdlgmkXOU55B\nFJkfKlUSO7rS6RQDeqILC6kj6OK1J5ZAALLsPrrsctnZZRXLABFxx7b0x0OmXa9UMxp7YvPcbY63\ncTg04VVrWA9WKjW2V0ls42RpqRxxj+X8dPp99BfI/pPbtYyy2KpIY0Bv1yteDOHOUOx2KO+T85Rn\nLGL2hKEaJ2NTJbE3oaLA0qWwZcv47fN4wD5jJ5i0cL4yZy65VjHscc4c0fhokD4uqLpAWm6wbYzM\nPAQiR+12Dx9xD9U4WVEx/oh7wwHZf+YWzeXg7txwEbVzG0O4w+gt5zWSPTYbWOvl2RJa7Jvp7u0m\nGBQ3myrciiJqfkybJqdK1K5dqnDX1sKpU6JBMF57YunqAnOVnJ+c7dS6oM2bB//4R1yHHJc9ySYT\n7bl8uuw/debN2HO7I09lXq94KhptxK2u6+4WEXf0GIGxnJ/Nx2X/WTlpJRUVcR9mUPR2veLFEO4M\nxW6H1qMzsXZrYWvI3MOmU5sGNE76fEKkCwqEoIaUEE3Fz/Cj/Z+l65rb+M27j9Dd282bb4p0yiuv\njN++QAD6y+Qbb2H+0EOVDVLPjIIZFCia//SbeuibtElKlQwWcVttIfb2P8Mdf7uDv2d/kp1Zj5Bl\n68bvF0FCd7fojjfe0Yo7zw7esG1gCHcEveW8RpPjPn4cKv1XSev/eeyfAxon29rEjeR0gqevhUse\nv4TTF3yU50/9ju5Zf+Ket7/Ekl8t4ZkNR7jlloFD5UdjTyzBIASK5IalxcWJu/Ey7XqlmtHaMztL\n9p/u8n8OK9w4WvhF16Wszfsoj+16jOOuJ/lTx5d4RFlCQ88R/H4h7upsRfHaE83+Ttl/YgcNjQe9\nXa94MYQ7Q7HZRMnNuRb5xlt3fN2AxsnW1nAfbs5Sf3U1b9a+OeB4R9uO8rz7Cj52e2tC+t82edvp\ncR3VVihmlpQtHfoDBmlhvlX2n/aidZFUic8nUiVqg2VTVyObZ1VzrGdgI0iLcpRn7FdS29qK0ynE\nezxjBNr97TT1af5jNpk5vyKj6tYlFUO4w+gt5zWSPfPmiXn1VhZdLvXH3de0D6/lyICIO78oyGfW\nXU9/0XtDHlPJreX7u79Ib+/AKaziPT/7WndKyzkdCynOG6FzbRxk2vVKNaO15zzH5ZgUzX+89n0c\naz8i3ocjbqsVfIEg/1n/ITqtQ/uPL+s039jwRRwOEVhER9zxnp+dDbL/LCxZiMPiGGLv+NHb9YoX\nQ7gzFHVkWIm7gEumXCJt65j8ZynibmuD0wu+zs5G+dHzwspLKWq+QVr3zP5nsM3dNGAEXby81y5/\nV1bjCqnyn4E+KLAXUBaU/ef1tj8DmnDbbPDn9v/DiR75ml469VIctddL614++QyhKa+PO+LeXp+8\nNMlEwBDuMHrLeY1kj9MJ550HCxfCrefdKm3rmvsoDldfRLhfPvMHjhf9Ston68TV/O0ja1l27Blm\nOZZJ2/ov/FEkXfKlL8H998d/fg565IYlpS6xwp1p1yvVjNYeqxUmd8r+s8n3KH2hvohwH3X9gS3B\nX0v75LVcxdrb1mL7+7MsKZGLPnWe92Opl0k89qgMqOGeYOHW2/WKF0O4M5i9e+Hyy+GjCz+KLcsW\nWR9y1/JG+1MEg7Dl9Bb+5P289LmpuTMwPfcXch02HFYLt1c8LG0PTnmFPfUHAXjkEW0Ch3g40iXf\neL2nVhoRtw6x2aCs5aOYQ5r/dCi1PLXvKXw+aLRu4TWb7D9VjhlMevNprFk2PO0Wfnq17D++ilfo\ntBwcV6+SWOFeWWn0SIrGEO4west5xWNPob2QWxfcJq37ya7/i2/aU9z4lxvpR5v2ydRn478vfY4+\nX36kH/d08yU42uTBPI/v/3nk/ZQp8dnT3NVMS98p7TtDFpSzi7FYRn2IEcnk65UKRmuP1QpKdyFl\nZ2X/+dZr32Kv8hS/9dxIv0nzn2zFxiOXPUd3Wz7d3aIc7+WzLmaBWx7Ms830cyniHq09oRAca2jm\nVKfmPxazZcDkD+NFb9crXgzhniB86+JvQb+mjI3dDQQ/9HFauuW+fRU7fkuFaSk5OaLanvpIa9r6\ndWm/l2qfoKVTJLqjS62OhthoKadjES6b1RjxpkPsdtHvuuzot8g2af5T761nS8XH8YZk/7nB/FtW\nTVmKz6fVKQH42DTZf3b0PoGvJ/6GkrVr4dY7Zf9ZVLYIa7Y17mNNZAzhDqO3nFe89swrnQVvfnPY\nfe659B4qmm+jvV0rp2q3i2HLvXtuptJdGdk3EOrid5vF9KGBQHz2xAo3dYlPk2T69Uo2o7XH5QqP\npm2bxadmDe8/FwTvZZXtNtxu0VWwvV0rs3vNlA9j8Wv+E1S6OGp+KbI8WntOnIA6JflpEr1dr3gx\nhHsCYX/7Aa6c/MFBt91ccScPVD+A0yluOHUeR5tNDHUvKbTw8fM+Ln3m78efAuKfzSS2R0DwhNGj\nRK+4XEKE/X74+pIHWOK4btD9Fnf9K8u990eGvPf2Qn29NiORy27BfUr2n2P2p+K2p64OOpxGj5KR\nMIQ7jN5yXmOxx5aTzX+ufB7Xmz9hXvE88BdySVU1s7e/xDeXPITJZMLpFN0DY4W7uHhg75Rt7f+g\nuKoDrzc+ewZE3PWJF+6JcL2SyWjtUYXb64WCvGy+M+MFFtb9J/OK52EOFLKqdA1fLXqR5S0/pbfH\nhNWqzaR+7BiRSn02G9iPyf7T4PwHHYGOuOw5cwYChcntURKPPXrFEO4JhNUK3b5sCg/exYEvH6Do\n0Vaeu34j5qPXkSuK8kWEOzpVogr38orlzCyYGTlen9KDbekLcc0EX+epo8HXEFm2ZdmgaeGIhe0N\n0oMq3B6PSHvkurKpPPkNDnz5AI5ftvLPT9awKv+DBINarRL1c8ePa8JttUKobjml2Zr/hMw9vHDw\nhbjsOdZUh+LS/Mdqtg2oG25gCHcEveW8xmKPzSYajNSby2oVN5vHI/rjAkNG3CUlYDKZBkTdwRnP\n4/WO3p7YaHtJ+VIIWZg9O+5/Z1gmwvVKJvHkuD0e0UDpdGrD27u7RTpEHTk5mHBHR9xWK/QETSy3\nyf7z/EExSeisWdW88cbI9pzokf1nfuFSLFkJ7I4URm/XK14M4Z5AWK1CuG02bTkY1AriAwNy3JMn\ni1rd6ryON8+/WTpmW/46PP7R9w4Y2P9WPOZ+8Yvx/z8GycdqFRX9XC4xqYY6A05zs8hfm0yDC7fb\nDUePyqmSQADOM8v+s+7YOrp6uvjb3+Ab3xjeFkWB5mzZf84vM/Lbg2EIdxi95bzGYo/VKqKn6Ijb\n7xc3ojrbjMMhC/f8+eJVFe6l5UspNE+NHLPfHMBXvpaNG0dnz7b6bdLyykkrOXwYLroo7n9nWCbC\n9Uomo7VHzVdH/7B3dYlJgtWGx9FG3MEglPQtJTek+U+gL8DaY2t5660a3nlHm2EpFIJfyYN5CQSg\nr0z2n1WTkjPwRm/XK14M4Z5ADJYqaW7WpiiDgTnuOXPENm0mdRPLHDfKB57/wqhGwYWUEFvPbJXW\nraxcmfA0iUFicTo14Y5UAhxBuN1usZ8q3BYL9PdDIGBiTkj2nxcOvkBrqxBrNV3S1CTKKYRC2n4d\nnSGokv3nomnGiMnBMIQ7jN5yXmOxJzZV4nKJNIia34aBqRK7XUwhpgo3wEWF8o2nzHqRhYveN+L3\nH2w5SGdQm6/Kac5nbvHcuP+P0TARrlcyicee2Ig7OlUCgwu3Wvq1qkq8qikVrxcWZsn+8+LhF+nn\nfZSXC8EGUfNdUZCKme06cxDFGjXfmT+f88rPDf+Jl/EKt1FgWUfEpkry8kS/WPWmhIGNkwCf+YyY\na1JlRenFWHqLIsuKrYMNxzeN+P1v1b4lLc91XiCVnDXQJy6XNpBmtBH3eefBHXdowg3aE9+snIsp\nsP7/9s4/Oory3OOfZRMSlhCSFBIQEgIEVHpAKQql4sH2BDGI12tV4LZHpd4rFlvs6dVbrL2nam1r\nPb2Hpl70XtQevfYee7DlQCtwquCBKiA/RCJXfooEaRQwgfwgwQgkc/94ZzIz6+5kZzezM9k8n3Ny\nZmd3dvabZ5599p3nfd/nNf2nqb2JI+fftC1WXV+vttZ1Kbcdt/tP+KT4TzxSscpcIN6qgQuA7wBL\ngV6xJGzQcl7J5ritLe78fDUuNjpwnz5tpkoAHn4YLrU0bAYPyqKw/ibbuf9n3fJuP3973Xbb/pcH\nT3f9PyRKJlwvL3Gjx9rizslRKY8jR2DECPO56MBdXQ3PP28/j9FwiORmMXu03X/qzi9n7FjnwP1u\nvd1/BjT0Hf9xSyqBey0Qq/pEEbAIeAF4GvhNCp8huCA6x52fr4b6RQfutjZ7aiSavDwYePwW23Pv\nntmCppkrbh8/rr7gVrZFtbgnFdkLDwnBxBq4QyFVVOzVV2GSXtcpVuCOhdFwyMmBm8fb0yUXhm+h\nbJT2hcBtnZX7f412/yloFf+Jhxf3IVcAh/THrUAFEPbgc3qUoOW8UslxWwN3XZ09x23MYHRaLTsv\nD/odm0W/DnO6Y/OIBnaf2N21f9ttsGWLenzxIrz2t2YONOw3T6KFmDzUXnGwJ8mE6+Ulyea4Aa65\nBk6ehCuuUPuJBu7cXDNVVzX+ejhvmS775QaaBuzuCtzGuqZGi7u5vZm6z+3+U9av7/iPW7I8OGcJ\nYJ1rdw4YApyKPnDhwoWUl5cDUFBQwJVXXtllUONWRvYT3z9zBlpariM3V+2fPg0ffXQdEyeaxw8c\nqI5vadnM5s2xz5eXB42f7mDge1M4+xV9GEAtVP+hmv99QBXnPnRIvX/mzOvYsQNuuGM5fEOD0erw\n7H2jqB25B2YExz6yH/96nzlj+sOMGfD665vZu1ftq07HzWRlQU5O/PNduKD8LycH3t25A97+CszU\nf91r4e2caqZmKf+pqVHvb2lR71/+ynK0WtN/qBlFf20P4L99vNivrq6mpqamK/71NLOBTTH+jAFe\nJ2K8ZxbwjGV/HxBr6pMWJDZt2uS3BBvJ6Fm8WNMqKjTtBz9Q+9XVmgaa9vDD5jG7dqnnVq2Kf57m\nZk0bNEjTSue+pPEo6u8utAlPT9A0TdPa2tQ5nntOHb9unaZRtcQ89lG0wfPv1w4dcv0vJEwmXC8v\ncaNn6VJNe+YZc/+TTzRtxQpzv6lJ+UNRkabV18c/z9VXa1pZmaatXKn2+19l959LfjFBW7hQvTZv\nnqYNHKhpzz6r9pest/sPN9yvLVmS8L/gmqBdL0CLESPj0l2L+zX9LxGygTxgK2DUh8wD6oAL8d4k\n9ByxOifBXk/bqBniVGO7Kw9+dC7hq8N0aCqZvb9+P4dPH0ZrGA+YkylOnQLGbLSd4/zByq5RCUKw\nefxxc5w/qDTaIsuiN0aqpLOz+xy3dVRTYcONNIRM//nkwn5OXTwMjKehAcaONVMlG4/a/YejlZTM\nSP1/y1RSyXHPAQoAY8G52cBPUKmRZ4F7gAeAJakITBfGLUxQSEZP9BfHKXA75bjDYXWOxk8KmT5c\n16Hfwq45uIaP9MVJGhvV9vDJj2HoAfMEnWE6js7sGmLmBZl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       "text": [
        "<matplotlib.figure.Figure at 0x7f79a86cbd50>"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The final plots shows the original signal (thin blue line), the filtered\n",
      "signal (shifted by the appropriate phase delay to align with the original\n",
      "signal; thin red line), and the \"good\" part of the filtered signal (heavy\n",
      "green line). The \"good part\" is the part of the signal that is not\n",
      "affected by the initial conditions."
     ]
    }
   ],
   "metadata": {}
  }
 ]
}